Agents used as phase-transfer catalysts are onium salts (ammonium and phosphonium salts), macrocyclic polyethers (crown ethers), aza-macrobicyclic ethers (cryptands), and open chain polyethers (polyethylene glycols, PEGS, and their dimethyl ethers, glymres) in the presence of dipolar aprotic solvents like dimethyl sulfoxide (DMSO), N-N-dimethylformamide (DMF), N-methyl-2-pyrrolidone, tetramethylurea, and so on in both soluble and quenched forms. A large number of phase-transfer-catalyzed reactions involving simple displacement reactions are carried out under neutral conditions, although some variants of the typical phase-transfer-catalyzed mechanism are possible. In the general case, the role of the phase-transfer catalyst (Q⁺X^-) is to function as a vehicle to transfer the anion (Y^-) of the metal salt (Y^-M⁺) from the aqueous or solid phase into the organic phase where it reacts with the organic substrate RX, giving the desired product RY and regenerating Q⁺X^-, which can continue the phase-transfer-catalyzed cycle. Carbenes are neutral compounds featuring a divalent carbon atom with only six electrons in its valence shell. Considering a prototype carbene -C ¨-, the carbon atom can be either linear or bent, each geometry describable by a certain degree of hybridization. The linear geometry implies a sp-hybridized carbene center with two nonbonding degenerate orbitals (p_x and p_y). Bending the molecule breaks this degeneracy and the carbon atom adopts an sp²-type hybridization: the p_y orbital remains almost un-changed (it is usually called p_π), while the orbital that starts as pure p_x orbital is stabilized since it acquires some s character (it is therefore called σ). The linear geometry is an extreme case; most carbenes are bent and their frontier orbitals will be systematically called σ and p_π. The energy state has one electron in the σ and one in the p_π, as for state, but with antiparallel spins.